Abstract:
ABSTRACT: An UV spectrophotometric method for the quantitative determination of Temozolomide (TMZ) in bulk and capsule was developed in present work. The parameters linearity, precision, accuracy, limit of detection and limit of quantitation were studied according to International Conference on Harmonization guidelines. UV spectroscopic determination was carried out at an absorption maximum of 328 nm using 0.1N Hydrochloric acid as solvent. In the UV spectroscopic method linearity over the concentration range of TMZ was found to be 2-18 μg/ml with a correlation coefficient 0.999. The limit of detection and limit of quantification were found to be 0.5271 and 1.6454 mg/ml respectively. Results of the analysis were validated statistically and by recovery studies. The proposed method is simple, rapid, precise, accurate and reliable and can be used for the routine quantitative analysis of TMZ in bulk and pharmaceutical formulation.

Abstract:
The idea that quantum gravity can be realized at the TeV scale is extremely attractive to theorists and experimentalists alike. This proposal leads to extra spacial dimensions large compared to the Planck scale. Here, we give a very systematic view of the foundations of the theories with large extra dimensions and their physical consequences.

Abstract:
Since it is not possible to optimize a standard relaying system to every protection need, Digital Multifunction protection systems are proposed as they have features like cost efficiency, functional flexibility, adaptive relaying and self checking capability. With the advantage of generally available hardware and software, having the speed and capability of digital relays necessary for protection application, it has now become possible for the relay engineers to develop and implement custom protection solutions for those applications where standard packages may not provide the necessary flexibility or performance. A modified Fullcycle Discrete Fourier Transform (FCDFT) Algorithm based digital multifunction relay is proposed which has capability of executing trip command by extracting exact fundamental frequency component, by eliminating harmonics and decaying DC offset component, during faults in power systems. The proposed algorithm was tested for different faults on 220KV, 100km overhead transmission line. Electromagnetic Transient Program (EMTP) and Power System Computer Aided Design (PSCAD) were used to generate waveforms under different fault locations and fault inception angles. The results show that the proposed Digital multi-function relay worked efficiently and reliably.

Abstract:
In this article, a broad perspective of supernovae, their classification and mechanism is given. Later, the astrophysical significance of supernovae is discussed in brief.

Abstract:
It is a brief review of the physical theories embodying the idea of extra dimensions, starting from the pre-historic times to the present day. Here we have classified the developments into three eras, such as Pre-Einstein, Einstein and Kaluza-Klein. Here the views and flow of thoughts are emphasized rather rigorous mathematical details. Majour developments in Quantum field theory and Particle physics are outlined. Some well known higher dimensional approaches to unification are discussed. This is concluded with some examples for visualizing extra dimensions and a short discussion on the cosmological implications and possible existence of the same.

Abstract:
This is a pedagogical introduction to original Kaluza-Klein theory and its salient features. Most of the technical calculations are given in detail and the nature of gravitons is discussed.

Abstract:
The generic quadratic form of even dimension n with trivial discriminant over an arbitrary field of characteristic different from 2 containing a square root of -1 can be written in the Witt ring as a sum of 2-fold Pfister forms using n-2 terms and not less. The number of 2-fold Pfister forms needed to express a quadratic form of dimension 6 with trivial discriminant is determined in various cases.

Abstract:
Let $G$ be an edge colored graph. A {\it}{rainbow path} in $G$ is a path in which all the edges are colored with distinct colors. Let $d^c(v)$ be the color degree of a vertex $v$ in $G$, i.e. the number of distinct colors present on the edges incident on the vertex $v$. Let $t$ be the maximum length of a rainbow path in $G$. Chen and Li showed that if $d^c \geq k$, for every vertex $v$ of $G$, then $t \geq \left \lceil \frac{3 k}{5}\right \rceil + 1$ (Long heterochromatic paths in edge-colored graphs, The Electronic Journal of Combinatorics 12 (2005), # R33, Pages:1-33.) Unfortunately, proof by Chen and Li is very long and comes to about 23 pages in the journal version. Chen and Li states in their paper that it was conjectured by Akira Saito, that $t \ge \left \lceil \frac {2k} {3} \right \rceil$. They also states in their paper that they believe $t \ge k - c$ for some constant $c$. In this note, we give a short proof to show that $t \ge \left \lceil \frac{3 k}{5}\right \rceil$, using an entirely different method. Our proof is only about 2 pages long. The draw-back is that our bound is less by 1, than the bound given by Chen and Li. We hope that the new approach adopted in this paper would eventually lead to the settlement of the conjectures by Saito and/or Chen and Li.

Abstract:
In 1972, Erd\"{o}s - Faber - Lov\'{a}sz (EFL) conjectured that, if $\textbf{H}$ is a linear hypergraph consisting of $n$ edges of cardinality $n$, then it is possible to color the vertices with $n$ colors so that no two vertices with the same color are in the same edge. In 1978, Deza, Erd\"{o}s and Frankl had given an equivalent version of the same for graphs: Let $G= \bigcup _{i=1}^{n} A_i$ denote a graph with $n$ complete graphs $A_1, A_2,$ $ \dots , A_n$, each having exactly $n$ vertices and have the property that every pair of complete graphs has at most one common vertex, then the chromatic number of $G$ is $n$. The clique degree $d^K(v)$ of a vertex $v$ in $G$ is given by $d^K(v) = |\{A_i: v \in V(A_i), 1 \leq i \leq n\}|$. In this paper we give an algorithmic proof of the conjecture using the symmetric latin squares and clique degrees of the vertices of $G$.